Issue 50

N. A. Fountas et alii, Frattura ed Integrità Strutturale, 50 (2019) 584-594; DOI: 10.3221/IGF-ESIS.50.49 592 Figure 8 : Pareto front of the non-dominated optimal solutions obtained by the multi-objective grey wolf algorithm. Nevertheless, it is reasonable to argue that the suitability of the different non-dominated solutions provided by the optimiza- tion process is to be decided by the process engineer with regard to particular requirements or constraints. This is beneficial to the increase of production rates by reducing machining time as well. For the purpose of optimizing turning parameters in order to minimize Ra, Rt and Fc a population of 20 grey wolves and a maximum number of 250 iterations were selected. The multi-objective grey wolf algorithm was run several times inde- pendently to examine the variability in terms of the obtained results. It was deduced that the algorithm maintains repeatability in converging to the same optimal values despite its stochastic nature. The convergence diagram of the algorithmic evalu- ations is illustrated in Fig.9. It is shown that the algorithm is capable of obtaining the optimal solution for the three objectives by determining smaller numbers for both candidate solutions and interactions. Apparently the latter depends on the problem’s characteristics; optimization trade off (i.e. simultaneous minimization and maximization of several objectives) and settings for algorithm-specific parameters. The optimal solutions the algorithm obtains refer to alpha, beta and delta wolves holding the best positions in the Pareto front. According to the outputs and the related archive with the resulting costs, the best point of alpha wolf is for Ra = 3.025 μm; Rt =16.804 μm and Fc =83.209 N . The values for turning parameters corresponding to these results are 1600 rpm for n ; 0.1184 mm/rev for f and 0.6182 mm for a . The best point of beta wolf is for Ra =3.108 μm ; Rt =17.180 μm and Fc =83.153 N . The values for turning parameters corresponding to these results are 1313 rpm for n ; 0.1741 mm/rev for f and 0.5000 mm for a . The best point of delta wolf is for Ra = 2.966 μm; Rt =16.594 μm and Fc =83.326 N. The values for Figure 9 : Convergence speed during the algorithmic evaluations performed by the multi-objective grey wolf algorithm. 250 225 200 175 150 125 100 75 50 25 1 140 130 120 110 100 90 80 Objective evaluation number Pareto objective value